First do a check on what is offered in your area.
IDPA.com, USPSA.org, will probably be the easiest matches to find.
No sense in gearing up for something and not being able to find a place that offers it.
Generally, the clubs listed at the above organizations will offer other kinds of matches, too.
Like some kind of steel challenge, maybe, or bowling pin games, home made action matches, 'etc.
But check with IDPA and USPSA, first.